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| Home > Publications database > Numerical and analytical interpretation of rotation and radial electric fields in collision dominated edge plasmas |
| Book | PreJuSER-23575 |
; ; ;
2002
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag
Jülich
Please use a persistent id in citations: http://hdl.handle.net/2128/245
Report No.: Juel-3958
Abstract: The ambipolarity constraint and the parallel momentum balance equation of neoclassical theory, accounting for finite Larmor radius effects and inertia, allow to describe the radial electric field and the related spin up in collision dominated edge - plamas with steep gradients. Thus they may contribute significantly to the understanding of the L-H transition. The variation of the toroidal velocity from the last closed magnetic surface up to a position r within the plamma is predicted to be proportional to the integral of the product u$_{\theta} \frac{\partial lnT}{\partial r}$ i.e., to $\sum_{d}$ [$\frac{T^{' 2}_{i}} {{T_{i}}}$] L$_{d}$if the interaction with the neutral gas can be neglected. The summation is over different radial domains, such as the edge pedestal. L$_{d}$ is the radial extension of the respective domain. The dimensionless parameter $\Lambda$ = $\frac{\nu_{i}q^{2}R^{2}}{\Omega_{i}rL_{Ti}}$ = $\frac{\widehat{\nu}_{i}a_{i_p}}{L_{Ti}}$ [where $\widehat{\nu}_{i}$ = $\frac{qR \nu}{c_{i}}$ > 0.22 is the relevant collision parameter and a$_{i_p}$ip the poloidal ion Larmor radius] characterizes the ratio of the diamagnetic rotation frequency to the heat diffusion rate along magnetic field lines. Conventional neoclassical theory assumes $\Lambda \rightarrow$ 0. However, e. g. in ALCATOR C-MOD ohmic H-mode pedestals, $\Lambda$ is sufficiently large that conventional neoclassical results are invalid: it follows from the neoclassical theory that the poloidal velocity decreases below the Standard prediction $\upsilon_{neo}$ = $\frac{-1.83T^{'}_{i}}{eB}$ as $\Lambda^{2}$ increases and changes sign for $\Lambda^{2}$ = $\Lambda^{2}_{0}$ (typically $\approx$ 1-2). The equations are treated analytically using a linear interpolation for the poloidal velocity, $\upsilon_{\theta}$($\Lambda^{2}$), based an $\upsilon_{\theta}$($\Lambda^{2}_{0}$) = 0 and an the neoclassical value $\upsilon_{neo}$ for Small $\Lambda$. This allows to account for finite $\Lambda$ effects in the just mentioned integration. The equations are also solved numerically (1) to benchmark with a simplified analytical theory with $\Lambda$=0 and vanishing neutral gas density; (2) to compare with the analytical theory accounting for finite $\Lambda$ effects and (3) to explore the parameter space in regions where the analytical theory is not valid, in particular in the cases where the neutral gas density is larger than 10$^{14}$m$^{-3}$. The method resorts to an ODE - solver for the classical momentum balance which is combined with a solver for transcendental equations yielding $\upsilon_{\theta}$. The results concern the comparison with the analytical solution and the experimental results of the ohmically heated ALCATOR plasma. For $\Lambda$ = 0 the numerical solution and the analytical one agree exactly. For finite $\Lambda \approx$ 1 the deviations are surprisingly small. The toroidal spin up of the ALCATOR plasma, characterized by a very short decay length L$_{\psi}$, = 0.76 cm, is $\approx$ 40 $\frac{km}{sec}$. This compares well the measured value of 35 $\frac{km}{sec}$. The radial electric field profile assumes the characteristic shape and absolute values reported by the DIII-D Group.
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